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Question
Given: ∠GHE = ∠DFE = 90°,
DH = 8, DF = 12,
DG = 3x – 1 and DE = 4x + 2.
Find: the lengths of segments DG and DE.
Sum
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Solution
In ΔDHG and ΔDFE,
∠GHD = ∠DFE = 90°
∠D = ∠D ...(Common)
∴ ΔDHG ∼ ΔDFE
`=> (DH)/(DF) = (DG)/(DE)`
`=> 8/12 = (3x - 1)/(4x + 2)`
`=>` 32x + 16 = 36x – 12
`=>` 28 = 4x
`=>` x = 7
∴ DG = 3 × 7 – 1 = 20
DE = 4 × 7 + 2 = 30
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